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arxiv: 2509.01892 · v2 · submitted 2025-09-02 · 🪐 quant-ph

Accelerating BP-based decoders for QLDPC Codes with Local Syndrome-Based Preprocessing

Wenxuan Fan , Yasunari Suzuki , Gokul Subramanian Ravi , Yosuke Ueno , Ilkwon Byun , Koji Inoue , Teruo Tanimoto This is my paper

Pith reviewed 2026-05-18 20:22 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum error correctionQLDPC codesbelief propagationsyndrome preprocessingdecoding accelerationbivariate bicycle codefault-tolerant quantum computing
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The pith

A local syndrome preprocessing step accelerates BP-based decoders for QLDPC codes by up to 10 times on the [[144,12,12]] code while preserving or improving logical error rates.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that a lightweight preprocessing step can scan the syndrome for local patterns that flag trivial error events and pass them as hints to BP-based decoders. This targets the iterative BP stage that dominates decoding latency in quantum low-density parity-check codes. The hints speed convergence, cutting overall decode time on the bivariate bicycle code [[144,12,12]] at low physical error rates. The approach delivers a 10× speedup for BP-OSD and more than 2× for BP-LSD and Relay-BP, while holding logical error rates steady or lowering them. Readers would care because shorter decoding times reduce the overhead that currently limits fault-tolerant quantum computing.

Core claim

The authors establish that local patterns in the syndrome can identify likely trivial error events and supply them as hints to BP-based decoders for QLDPC codes. This preprocessing accelerates BP convergence and reduces overall decoding time. On the bivariate bicycle code [[144,12,12]] at low physical error rates, the method achieves a 10× speedup in decoding time for BP-OSD and more than 2× speedup for both BP-LSD and Relay-BP. It maintains the logical error rate when combined with BP-OSD and Relay-BP, while achieving a significant reduction in logical error rate when combined with BP-LSD.

What carries the argument

Local syndrome pattern detection that identifies trivial error events and supplies them as hints to accelerate BP convergence

If this is right

  • Decoding time for BP-OSD on the [[144,12,12]] code drops by a factor of 10 at low physical error rates.
  • Decoding time for BP-LSD and Relay-BP drops by more than a factor of 2 at low physical error rates.
  • Logical error rate remains unchanged when the preprocessing is added to BP-OSD or Relay-BP.
  • Logical error rate drops further when the preprocessing is added to BP-LSD.
  • The preprocessing step works as a compatible front-end for multiple existing BP-based decoder variants.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same local-pattern hinting could be tested on other QLDPC code families and larger distances to check generality.
  • Lower per-shot decoding latency may allow quantum processors to run error-correction cycles at higher repetition rates.
  • Hardware implementations of BP could incorporate this preprocessing directly to reduce both latency and power.
  • Similar local-pattern hinting might be explored for classical LDPC decoders used in communication systems.

Load-bearing premise

Local patterns observed in the syndrome can be used to reliably identify trivial error events that can be supplied as hints without increasing the logical error rate or harming convergence on non-trivial errors.

What would settle it

An increase in logical error rate when the hints are applied to the [[144,12,12]] code at the tested low physical error rates would disprove the central claim.

Figures

Figures reproduced from arXiv: 2509.01892 by Gokul Subramanian Ravi, Ilkwon Byun, Koji Inoue, Teruo Tanimoto, Wenxuan Fan, Yasunari Suzuki, Yosuke Ueno.

Figure 1
Figure 1. Figure 1: Workflow of the proposed preprocessing decoder. To reduce the latency of BP decoding, an intuitive ap￾proach is to explore preprocessing methods (prior to BP￾OSD decoding) that can provide information to the BP de￾coder, thereby helping it break ties and converge to solutions more quickly. For the surface code, such preprocessing meth￾ods have already been proposed, for example, Promatch [1], which sparsif… view at source ↗
Figure 2
Figure 2. Figure 2: Decoding time breakdown of BP and OSD un￾der varying physical error rates for BB codes with different code distances and BP iteration limits. The x-axis shows the physical error rate; the numbers in parentheses denote the code distance 𝑑 and the configured maximum BP iteration count. Specifically, distance-6 corresponds to the BB code [ [72, 8, 6]] and distance-12 corresponds to [ [144, 12, 12]]. error rat… view at source ↗
Figure 3
Figure 3. Figure 3: Logical 𝑍-error rate of BB codes [ [72, 8, 6]], [ [90, 8, 10]] and [ [144, 12, 12]] at a physical error rate of 0.6%, shown for various configured maximum BP iteration counts. The key takeaway is that, in practice, we should appropri￾ately increase the BP iteration limit to reduce logical errors— doing so shifts most of the decoding time back to BP. This trade-off motivates our work, which aims to cut down… view at source ↗
Figure 5
Figure 5. Figure 5: 1. Find associated data qubits (lines 6-7). Given the current detector𝐷 (marked in red square in [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: Four step-by-step examples of error propagation through gates in BB code syndrome extraction circuits: (a) 𝑋𝐼 Error on CNOT Gate 𝑃 (b) 𝑋𝑋 Error on CNOT Gate 𝑃 (c) 𝑋𝑍 Error on CNOT Gate 𝑄 (d) 𝑋𝑌 Error on CNOT Gate 𝑄. 1 D 4 2 6 3 5 Data qubit D 2 1 3 4 5 6 a1 b1 a2 b2 a3 b3 b4 b5 b6 a6 a5 a4 Cycle j+1 ⨁ j+2 Cycle j ⨁ j+1 (a) (b) Cycle j ⨁ j+1 Cycle j ⨁ j+1 2 1 3 4 5 6 a’1 b’1 a’2 b’2 a’3 b’3 b’4 b’5 b’6 a’6 … view at source ↗
Figure 5
Figure 5. Figure 5: Step-by-step illustration of local error event detection in the preprocessing decoder. This process analyzes XORed detectors across adjacent measurement rounds to identify error patterns. 3. Collect next detector values (line 9). We then mea￾sure the same check qubits in cycle 𝑗 + 2. By XORing the measurement results from cycles 𝑗 + 1 and 𝑗 + 2, we obtain the next set of detector values, denoted 𝑎 ′ 𝑖 , 𝑏 … view at source ↗
Figure 6
Figure 6. Figure 6: Breakdown of CNOT gate error syndrome patterns and coverage of the “XOR = 111” signature. CNOT error patterns, we can detect CNOT errors similar to those illustrated in [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Overall evaluation process The overall procedure is shown in [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Decoding performance comparison between the preprocessing decoder and the baseline BP-OSD decoder. (a) relative iteration count (b) relative decoding latency syndrome patterns for error detection. As the physical error rate increases, error patterns become more complex, making it more difficult for preprocessing alone to resolve errors. Consequently, the performance improvement diminishes at higher error r… view at source ↗
Figure 11
Figure 11. Figure 11: Impact of modifying the channel probability vec￾tor on logical error rate for the [ [72, 8, 6]] code under differ￾ent configured maximum iteration limits for BP. To analyze this, we performed a detailed investigation, as shown in [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Improvement in BP convergence probability and reduction in OSD runtime between the preprocessing decoder and the baseline BP-OSD decoder under different configured maximum iteration limits. [5] S. B. Bravyi and A. Yu. Kitaev. 1998. Quantum codes on a lattice with boundary. arXiv:quant-ph/9811052 [quant-ph] https://arxiv.org/abs/ quant-ph/9811052 [6] Nikolas P. Breuckmann and Jens Niklas Eberhardt. 2021. Q… view at source ↗
read the original abstract

Due to the high error rate of qubits, detecting and correcting errors is essential for achieving fault-tolerant quantum computing (FTQC). Quantum low-density parity-check (QLDPC) codes are one of the most promising quantum error correction (QEC) methods due to their high encoding rates. BP (Belief Propagation)-based decoders are widely used and highly competitive for QLDPC codes because BP offers inherent parallelism and strong scalability. However, BP-based decoders still suffer from high decoding latency, a large portion of which is spent in the iterative BP stage. In this paper, we propose a lightweight preprocessing step that utilizes local patterns in the syndrome to detect likely trivial error events and provide them as hints to BP-based decoders. These hints accelerate BP convergence and thereby reduce the overall decoding time. The proposed preprocessing step offers a broadly compatible approach to reducing the latency of BP-based QLDPC decodes. On the bivariate bicycle code $[[144,12,12]]$ at low physical error rates, our method achieves a $10\times$ speedup in decoding time for BP-OSD, and more than $2\times$ speedup for both BP-LSD and Relay-BP. Our method maintains the logical error rate when combined with BP-OSD and Relay-BP, while further achieving a significant reduction in logical error rate when combined with BP-LSD.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes a lightweight local-syndrome preprocessing step that identifies likely trivial error events from short syndrome patterns and supplies them as hints to BP-based decoders (BP-OSD, BP-LSD, Relay-BP) for QLDPC codes. The goal is to accelerate convergence of the iterative BP stage without degrading logical error rate. On the bivariate bicycle code [[144,12,12]] at low physical error rates, the method is reported to deliver a 10× speedup for BP-OSD and >2× speedups for the other two decoders, while preserving logical error rate for BP-OSD and Relay-BP and further lowering it for BP-LSD.

Significance. If the empirical gains hold under broader testing, the preprocessing offers a practical, decoder-agnostic way to reduce the dominant latency component of BP-based QLDPC decoding, which remains a central obstacle to scalable fault-tolerant quantum computation. The concrete speedups on a high-rate code and the reported compatibility with multiple post-processing variants constitute a tangible engineering contribution; the absence of additional free parameters is also a positive feature.

major comments (2)
  1. [§4 and abstract] §4 (Numerical Results) and the abstract: the logical-error-rate and runtime claims for the [[144,12,12]] code are presented without reported Monte Carlo trial counts, error bars, or statistical significance tests. Because the central claim is that the preprocessing maintains or improves LER while delivering large speedups, the lack of these details leaves open the possibility that the reported LER reduction for BP-LSD or the exact speedup factors are sensitive to sampling variance or post-hoc selection.
  2. [§3] §3 (Preprocessing Method): the assumption that local syndrome patterns reliably flag only trivial errors is load-bearing for the LER-maintenance claim. A concrete counter-example or false-positive analysis (e.g., weight-2 errors that produce the same short syndrome fragment) would be needed to show that the hints cannot steer BP toward an incorrect fixed point on non-trivial errors; the current empirical results on a single code and error model do not yet rule this out.
minor comments (2)
  1. [Figure 2] Figure 2 (or equivalent runtime-vs-p plot): axis labels and legend entries should explicitly state whether the plotted times include or exclude the preprocessing overhead; the current presentation makes it difficult to verify the net speedup.
  2. [§3] The description of the local-pattern detection rule would benefit from a short pseudocode listing or a worked example on a small syndrome fragment to make the implementation reproducible.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation and the specific comments that help improve the statistical presentation and methodological clarity of the work. We respond to each major comment below.

read point-by-point responses

  1. Referee: [§4 and abstract] §4 (Numerical Results) and the abstract: the logical-error-rate and runtime claims for the [[144,12,12]] code are presented without reported Monte Carlo trial counts, error bars, or statistical significance tests. Because the central claim is that the preprocessing maintains or improves LER while delivering large speedups, the lack of these details leaves open the possibility that the reported LER reduction for BP-LSD or the exact speedup factors are sensitive to sampling variance or post-hoc selection.

    Authors: We agree that explicit reporting of Monte Carlo trial counts, error bars, and measurement details would strengthen the claims. In the revised manuscript we will state the number of trials used for each LER data point on the [[144,12,12]] code, add binomial or Wilson-score error bars, and clarify that the reported speedups are averages over repeated independent runs with observed variation noted. These additions directly address concerns about sampling variance. revision: yes

  2. Referee: [§3] §3 (Preprocessing Method): the assumption that local syndrome patterns reliably flag only trivial errors is load-bearing for the LER-maintenance claim. A concrete counter-example or false-positive analysis (e.g., weight-2 errors that produce the same short syndrome fragment) would be needed to show that the hints cannot steer BP toward an incorrect fixed point on non-trivial errors; the current empirical results on a single code and error model do not yet rule this out.

    Authors: We acknowledge that the method is heuristic and that a dedicated false-positive analysis would be useful. The maintained or improved LER across the tested decoders already indicates that any misidentified patterns do not produce net decoding failures in practice. In the revision we will add a short discussion in §3 that includes a concrete example of a weight-2 error capable of generating a matching short syndrome fragment and explain why the subsequent BP iterations typically resolve such cases. A exhaustive theoretical enumeration of all false positives remains outside the scope of this engineering-focused paper. revision: partial

Circularity Check

0 steps flagged

No circularity: empirical speedups and LER results are measured outcomes, not derived by construction

full rationale

The paper proposes a local-syndrome preprocessing heuristic for BP-based QLDPC decoders and reports its effects through direct Monte Carlo simulation on the [[144,12,12]] bivariate bicycle code. Speedup factors (10× for BP-OSD, >2× for BP-LSD/Relay-BP) and logical-error-rate maintenance or reduction are presented as observed runtime and error statistics under the chosen error model, not as quantities obtained by fitting parameters to the target metrics or by renaming inputs. No self-citation chain, uniqueness theorem, or ansatz is invoked to force the central claims; the method is defined independently of the reported performance numbers and the results remain falsifiable by additional simulation or different codes.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard domain assumptions in quantum error correction rather than new free parameters or invented entities. The preprocessing step is an algorithmic addition whose correctness depends on the empirical reliability of local pattern detection.

axioms (1)
  • domain assumption Local patterns in the syndrome can be used to identify trivial error events that serve as useful hints for BP convergence
    The method presupposes that such patterns exist and can be detected quickly without introducing harmful false hints.

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Reference graph

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